Blender api: How to set shapekeys as keyframe in a loop?
Answering my own question as I figured it out. Just in case anyone else has a need for it, the below script works as expected.

import bpy

#save the total number of frames as var
frames = bpy.context.scene.frame_end + 1

#loop through frames, jump to each frame, add the armature, set as shapekey
for frame in range(frames):
    bpy.context.scene.frame_set(frame)
    bpy.ops.object.modifier_add(type='ARMATURE')
    bpy.context.object.modifiers["Armature"].object = bpy.data.objects["rig"]
    bpy.ops.object.modifier_apply(apply_as='SHAPE', modifier="Armature")

#for each frame, loop through shapekeys and add as keyframe per frame, set value to 1 if current frame = corresponding shapekey
for frame in range(frames):
    for shapekey in bpy.data.shape_keys:
        for i, keyblock in enumerate(shapekey.key_blocks):
            if keyblock.name != 'Basis':
               curr = i - 1
               if curr != frame:
                   keyblock.value = 0
                   keyblock.keyframe_insert("value", frame=frame)
               else:
                   keyblock.value = 1
                   keyblock.keyframe_insert("value", frame=frame)